The hour hand and the minute hand of Big Ben, the Elizabeth Tower clock in London, are 2.70 m and 4.50 m long and have masses of 60.0 kg and 100 kg, respectively.
(a) Determine the total torque due to the weight of these hands about the axis of rotation when the time reads the following. (You may model the hands as long, thin, uniform rods. Let positive torque correspond to the counterclockwise direction. Your answers must be accurate to within 10 N · m.)
(i) 1:00 N · m
(ii) 5:20 N · m(iii) 4:00 N · m
(iv) 8:20 N · m
(v) 10:50 N · m
(b) Determine all times when the total torque about the axis of rotation is zero. Determine the times to the nearest second, solving a transcendental equation numerically. (Do this using a computer. Your instructor may ask you to turn in this work. There are 24 unique times at which the torque is zero. Submit a file with a maximum size of 1 MB.)